Two possibilities
( 1)
Take point B as the vertical foot and make a straight line L 1 vertical BC.
From B(6, 1)C(3, 3), the analytical formula of the straight line BC is: Y=-2X/3+5.
That is, the slope of the straight line BC is K=-2/3.
Because the straight line BC is perpendicular to the straight line L 1.
So the slope of L 1 is K=3/2.
Because after B.
So the analytical formula of the straight line L 1 is: Y=3X/2-8.
Make a straight line L2 perpendicular to L 1 through point D.
Since L2 passes through point D, the slope is K=-2/3.
So the analytical formula of L2 line is: Y=-2X/3+ 19/3.
Solve the equation L 1, L2
X=86/ 13，Y=25/ 13。
That is, the intersection of L 1 and L2, that is, point A, A(86/ 13, 25/ 13).
(2)
Make a straight line L 1 vertical DC through point d.
Because c (3,3) d (2,5)
Therefore, the analytical formula of straight line DC is: Y=-2X+9.
That is, the slope of the straight line CD is: K=-2.
Because the straight line DC is perpendicular to the straight line L 1.
So the slope of L 1 is: K= 1/2.
Because L 1 intersects with point d,
Therefore, the analytical formula of the straight line L 1 is: Y=X/2+4.
Make a straight line L2 perpendicular to L 1 through point B.
So the slope of the straight line L2 is: K=-2.
Because the straight line L2 passes through the point b,
Therefore, the analytical expression of line L2 is: rate Y=-2X+ 13.
Equation solving line L 1, L2
X= 18/5，Y=29/5。
That is, the intersection of L 1 and L2, that is, points A, A( 18/5, 29/5).